{VERSION 2 3 "LINUX INTEL UNIX" "2.3" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 1" 0 3 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 }1 0 0 0 6 6 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Plot" 0 13 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Title" 0 18 1 {CSTYLE "" -1 -1 " " 1 18 0 0 0 0 0 1 1 0 0 0 0 0 0 }3 0 0 -1 12 12 0 0 0 0 0 0 19 0 }} {SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT -1 40 "75045 Dynamical systems: \+ Exam 1998-05-19" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 77 "This file cont ains direction field plots for each of the systems in the exam." }}} {SECT 1 {PARA 3 "" 0 "" {TEXT -1 9 "Problem 3" }}{EXCHG {PARA 0 "" 0 " " {TEXT -1 181 "As far as I know, Maple does not contain any good rout ines for drawing the stable and unstable manifolds at a saddle point i n the plane. So we'll settle for a direction field here." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "ODE3:=[diff(x(t),t)=x^2-y^2,diff(y( t),t)=1-x^2-y^2];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%ODE3G7$/-%%dif fG6$-%\"xG6#%\"tGF-,&*$F+\"\"#\"\"\"*$%\"yGF0!\"\"/-F(6$-F3F,F-,(F1F1F /F4F2F4" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 97 "DEtools[DEplot]( ODE3, [x(t),y(t)],t=-2..2,x=-1.5..1.5,y=-1.5..1.5,\n dirgrid=[30,30], color=blue);" }}{PARA 13 "" 1 "" {INLPLOT "6%-%'CURVESG6acn7%7$$!#:!\" \"$!+ieF[9!\"*7$F($!+QTs^:F-7$$!+m*oq[\"F-$!+HpKH:F-7%7$$!+!)*Hu6F-$!+b*R1X\"F-7$$!+1R607F-$!+X+O\\:F-7$$!+n+3'=\"F-$!+-7&=`\" F-7%7$$!+**)e`1\"F-$!+mMm_9F-7$$!+$*[026F-$!+MlLZ:F-7$$!+7L>'3\"F-$!+8 70K:F-7%7$$!+2gAo&*!#5$!+f$[_X\"F-7$$!+RYp35F-$!+T;vW:F-7$$!+I5wi)*Fdp $!+Z\")[)Fdp$!+w>Ae9F-7$$!+$pf!)4*Fdp$!+C!y[oFdp$!+vFbH:F-7%7$$!+uc4*G&Fdp$!+z_Fn9F-7$$!+cY@!4' Fdp$!+@ZsK:F-7$$!+0b&\\$eFdp$!+)[o&G:F-7%7$$!+v4oNUFdp$!+%>S(p9F-7$$!+ PQmu]Fdp$!+1)f-`\"F-7$$!+0#pt\"[Fdp$!+7UkF:F-7%7$$!+?yO(=$Fdp$!+oivr9F 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